Extrinsic phonon thermal Hall transport from Hall viscosity

摘要: Motivated by recent experiments on the phonon contribution to thermal Hall effect in cuprates, we present an analysis of chiral transport. We assume behavior arises from a non-zero vicosity, which is likely induced coupling electrons. Phonons with viscosity have intrinsic conductivity, but Chen et al. (Phys. Rev. Lett. 124, 167601 (2020)) argued that significantly larger conductivity can arise extrinsic inversely proportional density impurities. solve Boltzmann equation for transport and compute temperature ($T$) dependence originating skew scattering off point-like find dominant source interference between impurity channels opposite parity. The $\sim T^{d+2}$ at low $T$ $d$ dimensions, has window $T$-independent $T > T_{\rm imp}$, where $T_{\rm imp}$ determined ratio potentials also consider role non-specular sample boundary, it leads negligible corrections $T$.